Indirect estimation of alpha-stable distributions and processes
AbstractThe alpha-stable family of distributions constitutes a generalization of the Gaussian distribution, allowing for asymmetry and thicker tails. Its practical usefulness is coupled with a marked theoretical appeal, as it stems from a generalized version of the central limit theorem in which the assumption of the finiteness of the variance is replaced by a less restrictive assumption concerning a somehow regular behavior of the tails. Estimation difficulties have however hindered its diffusion among practitioners. Since simulated values from alpha-stable distributions can be straightforwardly obtained, the indirect inference approach could prove useful to overcome these estimation difficulties. In this paper we provide a description of how to implement such a method by using a skew-t distribution as an auxiliary model. The indirect inference approach will be introduced in the setting of the estimation of the distribution parameters and then extended to linear time series models with alpha-stable disturbances. The performance of this estimation method is then assessed on simulated data. An application on time-series models for the inflation rate concludes the paper.
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Bibliographic InfoPaper provided by Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" in its series Econometrics Working Papers Archive with number wp2004_07.
Length: 23 pages
Date of creation: 01 Jun 2004
Date of revision:
Indirect inference; Alpha-stable distributions; Heavy tails.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-05-23 (All new papers)
- NEP-ECM-2005-05-23 (Econometrics)
- NEP-ETS-2005-05-23 (Econometric Time Series)
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